The amount of Brine Fill establishes the amount of brine that is available. In post #27, you included a photo of the BLFC label which specifies the brine tank refill flow rate to occur during Brine Fill. Since each 1 gallon will dissolve 3 lbs salt, then a 0.5 gpm fill rate will result in 1.5 lbs of salt being dissolved for each 1 minute of fill.
The Brine Draw and Slow Rinse rates are governed by the injector that is installed. Each injector size is given a different colour and number to make it easier to identify and reference its flow rate.
The BD & SR process is combined together since slow rinse flow through the injector will create suction on the brine line to draw brine into the media tank. Once all of the brine has been drawn, an air check valve (floating ball) will close the brine pickup opening to prevent air from being drawn into the softener. Slow Rinse flow will continue so as to push the brine through the resin bed and eventually rinse remaining brine residue from the resin. While the Brine Draw/Slow Rinse setting is typically 60 minutes, brine should be all drawn from the brine tank within approx 15 minutes of that time. If the remaining slow rinse time is insufficient, the initial soft water flowing to the home's fixtures will be salty directly after each regeneration cycle.